If two lines are cut by a transversal so that a pair of corresponding angles are congruent, then the lines are parallel.

This statement is a postulate in geometry known as the Corresponding Angles Postulate. Here's the step-by-step explanation:

1. A transversal is a line that intersects two or more lines at different points.

2. When a transversal intersects two lines, it forms several pairs of angles. Among these are corresponding angles, which are angles that are in the same relative position at each intersection.

3. The Corresponding Angles Postulate states that if two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent (equal in measure).

4. The converse of this postulate is also true: If a pair of corresponding angles is congruent when two lines are cut by a transversal, then the lines are parallel.

So, in conclusion, if two lines are cut by a transversal so that a pair of corresponding angles are congruent, then the lines are indeed parallel. This is a fundamental principle in geometry.